Engineering topics

Moudgalya, Sanjay

Publications and source records attributed to Moudgalya, Sanjay.

9 records

DOE OSTI2024

Filling constraints on translation invariant dipole conserving systems

Systems with conserved dipole moment have drawn considerable interest in light of their realization in recent experiments on tilted optical lattices. Here, an important question for such systems is delineating the conditions under which they admit a unique gapped ground state that is consistent with all symmetries. Here, we study one-dimensional translation-invariant lattices that conserve U(1) charge and Z L dipole moment, where discreteness of the dipole symmetry is enforced by periodic boundary conditions, with L the system size. We show that in these systems, a symmetric, gapped, and non-degenerate ground state requires not only integer charge filling, but also a fixed value of the dipole filling, while other fractional dipole fillings enforce either a gapless or symmetry-breaking ground state. In contrast with prior results in the literature, we find that the dipole filling constraint depends both on the charge filling as well as the system size, emphasizing the subtle interplay of dipole symmetry with boundary conditions. We support our results with numerical simulations and exact results.

1-dimensional systems↗

DOE OSTI2020

Quantum many-body scars in a Landau level on a thin torus

We review a kinetically constrained pair-hopping model that arises within a Landau level in the quantum Hall effect. At filling ν = 1/3, the model exactly maps onto the so-called “PXP model,” a constrained model for the Rydberg atom chain that is numerically known to exhibit ETH-violating states in the middle of the spectrum or quantum many-body scars. Indeed, particular charge density wave configurations exhibit the same revivals seen in the PXP model. We generalize the mapping to fillings factors ν = p/(2p+1), and show that the model is equivalent to nonintegrable spin chains within particular constrained Krylov Hilbert spaces. These lead to new examples of quantum many-body scars which manifest as revivals and slow thermalization of particular charge density wave states. Finally, we investigate the stability of the quantum scars under certain Hamiltonian perturbations motivated by the fractional quantum Hall physics.

1-dimensional spin chains↗

DOE OSTI2020

η-pairing in Hubbard models: From spectrum generating algebras to quantum many-body scars

In this work, we revisit the η-pairing states in Hubbard models and explore their connections to quantum many-body scars to discover a universal scars mechanism. η-pairing occurs due to an algebraic structure known as a spectrum generating algebra (SGA), giving rise to equally spaced towers of eigenstates in the spectrum. We generalize the original η-pairing construction and show that several Hubbard-like models on arbitrary graphs exhibit SGAs, including ones with disorder and spin-orbit coupling. We further define a restricted spectrum generating algebra (RSGA) and give examples of perturbations to the Hubbard-like models that preserve an equally spaced tower of the original model as eigenstates. The states of the surviving tower exhibit a subthermal entanglement entropy, and we analytically obtain parameter regimes for which they lie in the bulk of the spectrum, showing that they are exact quantum many-body scars. The RSGA framework also explains the equally spaced towers of eigenstates in several well-known models of quantum scars, including the Affleck-Kennedy-Lieb-Tasaki model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Large classes of quantum scarred Hamiltonians from matrix product states

Motivated by the existence of exact many-body quantum scars in the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain, in this work we explore the connection between matrix product state (MPS) wave functions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wave function. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong eigenstate thermalization hypothesis. Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wave functions, and derive families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit types of exact quantum scars, including a $\textit{U}$(1)-invariant perturbed Potts model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Extension of the eigenstate thermalization hypothesis to nonequilibrium steady states

We extend the notion of the eigenstate thermalization hypothesis (ETH) to open quantum systems governed by the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation. We present evidence that the eigenstates of nonequilibrium steady-state (NESS) density matrices obey a generalization of ETH in boundary-driven systems when the bulk Hamiltonian is nonintegrable, just as eigenstates of Gibbs density matrices are conjectured to do in equilibrium. Furthermore, this generalized ETH, which we call NESS ETH, can be used to obtain representative pure states that reproduce the expectation values of few-body operators in the NESS. The density matrices of these representative pure states can be further interpreted as weak solutions of the GKLS master equation. Additionally, we explore the validity and breakdown of NESS-ETH in the presence of symmetries, integrability, and many-body localization in the bulk Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Operator spreading in quantum maps

Operators in ergodic spin chains are found to grow according to hydrodynamical equations of motion. The study of such operator spreading has aided our understanding of many-body quantum chaos in spin chains. Here we initiate the study of “operator spreading” in quantum maps on a torus, systems which do not have a tensor-product Hilbert space or a notion of spatial locality. Using the perturbed Arnold cat map as an example, we analytically compare and contrast the evolutions of functions on classical phase space and quantum operator evolutions, and identify distinct timescales that characterize the dynamics of operators in quantum chaotic maps. Until an Ehrenfest time, the quantum system exhibits classical chaos, i.e., it mimics the behavior of the corresponding classical system. After an operator scrambling time, the operator looks “random” in the initial basis, a characteristic feature of quantum chaos. These timescales can be related to the quasienergy spectrum of the unitary via the spectral form factor. Furthermore, we show examples of “emergent classicality” in quantum problems far away from the classical limit. Lastly, we study operator evolution in nonchaotic and mixed quantum maps using the Chirikov standard map as an example.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Exact excited states of nonintegrable models

We discuss a method of numerically identifying exact energy eigenstates for a finite system, whose form can then be obtained analytically. We demonstrate our method by identifying and deriving exact analytic expressions for several excited states, including an infinite tower, of the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model, a celebrated nonintegrable model. The states thus obtained for the AKLT model can be interpreted as from one to an extensive number of quasiparticles on the ground state or on the highest excited state when written in terms of dimers. Included in these exact states is a tower of states spanning energies from the ground state to the highest excited state. Here, some of the states of the tower appear to be in the bulk of the energy spectrum, allowing us to make conjectures on the strong eigenstate thermalization hypothesis. We also generalize these exact states including the tower of states to the generalized integer spin AKLT models. Furthermore, we establish a correspondence between some of our states and those of the Majumdar-Ghosh model, yet another nonintegrable model, and extend our construction to the generalized integer spin AKLT models.

1-dimensional spin chains↗

DOE OSTI2018

Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis

We obtain multiple exact results on the entanglement of the exact excited states of nonintegrable models we introduced in Phys. Rev. B 98, 235155 (2018). We first discuss a general formalism to analytically compute the entanglement spectra of exact excited states using matrix product states and matrix product operators and illustrate the method by reproducing a general result on single-mode excitations. We then apply this technique to analytically obtain the entanglement spectra of the infinite tower of states of the spin-S AKLT models in the zero and finite energy density limits. We show that in the zero energy density limit, the entanglement spectra of the tower of states are multiple shifted copies of the ground-state entanglement spectrum in the thermodynamic limit. We show that such a resemblance is destroyed at any nonzero energy density. Furthermore, the entanglement entropy S of the states of the tower that are in the bulk of the spectrum is subthermal S ∝ log L, as opposed to a volume law S ∝ L, thus indicating a violation of the strong eigenstate thermalization hypothesis (ETH). These states are examples of what are now called many-body scars. Lastly, we analytically study the finite-size effects and symmetry-protected degeneracies in the entanglement spectra of the excited states, extending the existing theory.

1-dimensional spin chains↗

DOE OSTI2015

A finite-time exponent for random Ehrenfest gas

We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit. - Highlights: • We present a finite-time exponent for particles moving in a plane containing polygonal scatterers. • The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle. • Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule. • Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗